Thomas Callister Hales

Thomas Callister Hales ( born June 4, 1958 in San Antonio, Texas, USA) is an American mathematician. It particularly deals with problems in the field of algebra and geometry. Hales was known in 1998 by his computer proof of Kepler 's conjecture beyond the borders of the mathematical community also.

Life

Hales to 1982 completed his studies in mathematics and engineering - Economic Systems from Stanford University with a Bachelor of Sciences and a Master of Sciences. This was followed by a one-year stay at the University of Cambridge, where he received a Certificate of Advanced Study in Mathematics (Part III of the Mathematical Tripos ). Since 1983 he worked at Princeton University under Robert Langlands in his doctoral dissertation on The Subregular Germ of orbital integral, from which he graduated in 1986. After completing his doctorate, he worked at the Mathematical Sciences Research Institute ( MSRI ) in Berkeley. After working as an assistant professor or visiting scholar at Harvard University (1987-1989), at the School of Mathematics at the Institute for Advanced Study in Princeton, New Jersey, (1989-1990 and 1994-1995) and the University of Chicago with Paul J. Sally (1990-1993) in 1993 he became first an assistant professor and later professor at the University of Michigan in Ann Arbor. He was Andrew Mellon Professor at the University of Pittsburgh in 2001.

In 2009 he received the proof of the Kepler conjecture the Fulkerson Prize ( as well as his former graduate student Ferguson ). In 2002 he was invited speaker at the International Congress of Mathematicians in Beijing (A computer verification of the Kepler conjecture ). He is since 2012 a Fellow of the American Mathematical Society.

Work

Due to the large amount of data and the complexity of the proof of the Kepler conjecture so far this but could not be fully verified. The experts of the proof (by Gábor Fejes Tóth ) are convinced in his own words " 99 percent " of the correctness of the proof, but abandoned after a few years of intensive work exhausted. The proof is based on a, by László Fejes Tóth already proposed route via linear programming. To him also Hales ' graduate student Samuel P. Ferguson was involved. The reviewers complained of the partially sketchy presentation of evidence in preprint form, who already had a circumference of about 200 pages, without the computer printouts. Hales and Ferguson gave at that time, even after years of work on the evidence to be too exhausted to bring this to a polished form, which Hales but caught up after the verdict of the experts. The Annals of Mathematics published the evidence despite the confession of the failure of reviewers, 2005. Originally a notice about the only nearly complete examination was also provided, which then accounted for yet. Instead, wrote the editor of the Annals that they would the human part of the computer -assisted proofs particularly important mathematical theorems print in the future, even if the computer code ( which the Annals featured on their website available ) was not checked completely satisfactory. The Annals of Mathematics essay was only an overview, a more complete publication, the preprint 1998 revised, was made in 2006 in a special issue of the journal Discrete & Computational Geometry in which the editor Gabor Fejes Toth and Jeffrey Lagarias thank also the peer reviewers and this partly give the names (which usually is extremely unusual because peer reviewers remain basically anonymous).

The proof was the discussion about the extent to which evidence similar to that of Hales and Ferguson, who rely much on computer support, in principle, are acceptable new impetus. Similar discussions have been conducted within the proof of the four - color theorem by Kenneth Appel and Wolfgang hook from 1977 or other computer -based evidence.

Therefore Hales to research ways as well as in areas of mathematics where proofs very complex and computer for checking the results are necessary to strictly mathematical proofs can be created. In particular, he tried to formalize his proof of Kepler 's conjecture so that it can be checked by automatic theorem provers such as John Harrison's HOL light in the Project flyspeck. Such a review is created by Hales but also the long term and should be done previously distributed computing on the web as other intensive computer calculations, for example in the SETI @ home project.

Prior to this evidence was another proof attempt of Wu- Yi Hsiang from about 1990, who was sharply criticized by Hales and others, and has been rejected around 1997 in the overriding consensus of thus employing mathematicians inadequate. Hsiang himself remained convinced of the validity.

Hales also demonstrated some other famous conjectures of geometry. 1999 Hales proved the honeycomb conjecture (Honeycomb Conjecture), which goes back to ancient times and thought that in a breakdown of the plane into regions of equal area in each case the total amount of edges is at least in the regular hexagonal honeycomb layout. With his student Sean McLaughlin he proved in 1998 the dodecahedral conjecture of Laszlo Fejes Toth, who suspects starting from the kiss number 12 of balls in three dimensions that derived from the configuration Voronoi polygon has at least the volume of a regular dodecahedron ( the corresponding is scaled to the problem). McLaughlin was only undergraduate student ( with a major in music, clarinet), and received the 1999 Frank and Bennie Morgan Prize for outstanding work of mathematics students.

Hales himself wrote a review article about the evidence and the history of the Kepler conjecture and related conjectures in the Notices of the AMS. The essay won the Chauvenet Prize in 2003.

Prior to his employment with geometry, he worked on issues of the Langlands program ( automorphic forms and p- adic groups).

Writings

• Jeffrey Lagarias (Editor), Hales, Ferguson: The Kepler conjecture. The Hales -Ferguson proof, Springer Verlag 2011
• Thomas Hales: A proof of the Kepler Conjecture. In: Annals of Mathematics. Volume 162, 2005, pp. 1063-1183 ( Section 5 is written with Ferguson, who Ausatz received the 2007 Robbins Prize of the AMS)
• Thomas Hales, Samuel Ferguson (Editor Gábor Fejes Tóth, Jeffrey Lagarias ): special issue of Discrete & Computational Geometry, Volume 36, 2006, No. 1 to the proof of the Kepler conjecture. where: Hales: Historical Overview of the Kepler Conjecture, pp. 5-20, Hales, Ferguson A Formulation of the Kepler Conjecture, pp. 21-69, Hales Sphere Packing, III. Extremal Cases, pp. 71-110, Hales Sphere Packing, IV Detailed Bounds, pp. 111-166, Hales Sphere Packings, VI. Tame Graphs and Linear Programs, pp. 205-265